Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C5×Dic32 |
| derived, Sylow | C32 ⋊ C2×C42×C5 |
| Hall | C32×C5 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C5 | D32 |
| commutator, hypocenter | C32 | C2×C42×C5 |
| Frattini | C22 | C2×C5×D32 |
| Fitting, socle, prime radical | C23×C32×C5 | C22 |
| cosocle | C22×C32 | C23×C5 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C23×C5 | |
486 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 248 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 3541);